1RIKEN Center for Developmental Biology, Kobe 650-0047, Japan. 2PRESTO, JapanScience and Technology Agency, Kawaguchi 332-0012, Japan. 3Institute for FrontierLife and Medical Sciences, Kyoto University, Kyoto 606-8507, Japan.†Present address: Center for Vascular and Developmental Biology, FeinbergCardiovascular Research Institute, Northwestern University Chicago, IL 60611, USA.‡Present address: Department of Neurology, Children’s Hospital of PhiladelphiaResearch Institute, Philadelphia, PA 19104, USA.§Deceased.*Corresponding author. Email: [email protected] (M.E.); [email protected] (S.O.)
Okuda et al., Sci. Adv. 2018;4 : eaau1354 21 November 2018
Strain-triggered mechanical feedback in self-organizingoptic-cup morphogenesisS. Okuda1,2,3*, N. Takata1†, Y. Hasegawa1‡, M. Kawada1, Y. Inoue3, T. Adachi3,Y. Sasai3§, M. Eiraku1,3*
Organogenesis is a self-organizing process of multiple cells in three-dimensional (3D) space, where macroscopictissue deformations are robustly regulated by multicellular autonomy. It is clear that this robust regulation re-quires cells to sense and modulate 3D tissue formation across different scales, but its underlying mechanismsare still unclear. To address this question, we developed a versatile computational model of 3D multicellulardynamics at single-cell resolution and combined it with the 3D culture system of pluripotent stem cell–derivedoptic-cup organoid. The complementary approach enabled quantitative prediction of morphogenesis and itscorresponding verification and elucidated that the macroscopic 3D tissue deformation is fed back to individualcellular force generations via mechanosensing. We hereby conclude that mechanical force plays a key role as afeedback regulator to establish the robustness of organogenesis.
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INTRODUCTIONDuring organogenesis, morphogens dynamically organize spatialpatterns of cell differentiation in three-dimensional (3D) tissues(1, 2). According to the pattern, individual cells generate characteristicmechanical forces to form the entire organ structure in 3D space (3–5).Many molecules have been identified as key signaling factors thatregulate each step of patterning and force generation. However, thesemolecular signals are not enough to explain the entire regulatorymech-anismofmorphogenesis. In particular, it is still unclear how individualcells sense and modulate the entire 3D tissue formation across differ-ent scales. Previous studies have revealed cellular mechanosensingmechanisms (6–8), which may also be involved in the cross-scale reg-ulatory mechanism of 3D tissue formation. Therefore, in this study,we focus on the mechanical aspect of morphogenesis and reveal therole of mechanical force in regulating 3D tissue formation across dif-ferent scales.
Recent progress in the stem cell field has enabled us to formvarious3D tissues in vitro (9, 10). For instance, we have reported a culturesystem of pluripotent stem cell–derived optic-cup organoids, whichwell recapitulates a typical process seen in vivo (11, 12); on the basisof theWnt antagonism, the distal part of optic vesicle (OV) differenti-ates into neural retina (NR), whereas the adjacent part becomes retinalpigment epithelium (RPE). According to the differentiation pattern,the NR invaginates into the surrounding RPE in the apically convexdirection. Subsequently, a hinge structure is formed along the bound-ary between the inner NR and outer RPE to generate a cup-like tissueshape. From a mechanical point of view, this stepwise process pro-ceeds autonomously without external forces from the surroundingssuch as lens placode and periocular mesenchyme.
To explain this self-organizing process, we have previously foundseveral key candidates of driving force and suggested a relaxation-
expansion model (11) that explains the mechanism of optic-cup for-mation through four sequential phases (fig. S1A). In phase 1, semi-spherical OV autonomously generates the differentiation patterncomposed of distal NR and the surrounding RPE. In phase 2, thedistal NR decreases its stiffness according to the reduction of apicalmyosin accumulation. In phase 3, the boundary between NR andRPE causes apical constriction, by which the NR is passively invagi-nated. In phase 4, the NR causes rapid proliferation and facilitatesthe NR invagination by itself. Although this model is consistent withprevious experimental findings, our further mechanical analyseshave prompted the investigation of more elaborate mechanisms.
In the present study, we elucidate a mechanical force that is fedback from macroscopic 3D tissue deformation to individual cellularforce generation during optic-cup morphogenesis. On the basis ofprevious mathematical models (13–19), we developed a versatile 3Dvertex model that adequately describes general 3D multicellular dy-namics at single-cell resolution. The in vitro culture of optic-cup for-mation enables us to observe and perturb specific cell behaviors in 3Dliving tissues, whereas the in silico recapitulation enables us to predictits mechanisms comprehensively (15, 16, 20, 21). By combining thein vitro and in silico approaches, we found key cell behaviors requiredfor the NR invagination and the subsequent hinge formation along theNR-RPE boundary and elucidate the key role of mechanical force in theself-organizing optic-cup formation.
RESULTSQuantitative simulations predict key mechanisms inoptic-cup morphogenesisTo elucidate mechanisms of 3D tissue morphogenesis, we attemptedto combine in vitro and in silico systems. The optic-cup formationis a complex 3D deformation process to form several characteristicstructures such as the apically convex, thickerNR, the adjacent, thinnerRPE, and the sharply wedged hinge structure at the NR-RPE bound-ary (Fig. 1, A to D). The optic-cup formation follows various single-cell behaviors in 3D space, such as cellular contraction, extension,stiffening, softening, adhesion, growth, rearrangement, division, andapoptosis (11). In particular, cells at the NR-RPE boundary form ananisotropic hinge shape (Fig. 1E and movie S1). These cell behaviorsdynamically change according to the differentiation state of individual
Fig. 1. Quantitative simulations of 3D multicellular dynamics during optic-cup morphogenesis. (A) Time-lapse imaging of in vitro optic-cup formation. (B) Immuno-staining assay of the in vitro optic cup. (C andD) Spatial pattern of Mitf intensity and the curvature and thickness of epithelium along the epithelial sheet in (B). (E) Shape ofin vitro single cell at NR and the NR-RPE boundary in day 9 (also shown in movie S1). (F) Quantities of cell behaviors obtained from experiments [morphologies weremeasured as shown in fig. S2; epithelial thickness and surface stiffness were partly obtained fromour previous study (11)]. (G) Geometric structures of OV and cells on the 3Dvertex model (described in fig. S3). Themodel involves several physical parameters, a part of which are given by experiments in (F), and the other unknown parameters areentirely varied in computational simulations. (H) Phase diagram resulting from computational simulations for all of the unknown physical parameters (enlarged in fig. S4).Several phenotypes in the phase diagram are verified to correspond to those resulting from pharmacological assays in experiments (fig. S5; in silico phenotypes also showninmovie S3). (I to K) Outer and cross-sectional views of the recapitulated optic-cup formation steps (movies S2 and S3). For this recapitulation, two key factors are required:the autonomous bending of NR in the apically convex direction and the constriction of the NR-RPE boundary along the apicobasal (lateral) direction (K). (L) Shape of in silicosingle cell at NR and the NR-RPE boundary, where apical surfaces are colored red. Tissue morphologies are shown in 3D coordinates with the distal-proximal (Di-P), dorsal-ventral (Do-V), and anterior-posterior axis in (G) and (I) and are projected on the plane normal to the anterior-posterior plane in (F), (J), and (K).
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cells fromOV toNR and RPE in a dorsoventrally asymmetric manner(2, 12, 22).
To understand the mechanisms of this morphogenesis, we devel-oped a versatile 3D vertex model that describes 3D multicellular dy-namics, involving all of the abovementioned single-cell behaviors(fig. S2). By approximating individual cell shapes to polyhedrons, thismodel can express the entire pattern of 3D compacted multicellulardynamics at a single-cell resolution in a physically andmathematicallyconsistent manner (18, 23). Thereby, this model enables us to predict3D tissue deformation based on physical interactions among cells.
Using the developed 3D vertex model, we performed computa-tional simulations based on experimental data. First, we developeda mechanical model of single-cell behaviors in 3D space that in-volves several physical parameters of individual cells such as spon-taneous volume/height/curvature, apical/basal surface stiffness, andproliferation/apoptosis rate, which dynamically change during theoptic-cup formation (Fig. 1G). Second, we had measured some ofthe physical parameters experimentally (Fig. 1F and fig. S3) and in-troduced them into this model. Last, we carried out computationalsimulations for all of the other unsettled parameters by assuming aquasi-static deformation process and predicted effects of individualsingle-cell behaviors on the optic-cup formation (Fig. 1H, enlargedin fig. S4). The computational simulations succeeded in recapitulatingthe 3Ddeformation process of the optic-cup formation at the single-celllevel (Fig. 1, I to K, and movies S2 and S3), which included the apicallyconvex NR and the sharply wedged hinge structure along the NR-RPEboundary as well as the cell morphologies in columnarNR cells, cuboidalRPE cells, and hinge boundary cells (Fig. 1L), respectively.
The computational simulations also produced a variety of pheno-types with respect to a set of parameters (fig. S4 and movie S4). Thisis noteworthy since the importance of retinal differentiation and cellproliferation in optic-cup formation has been pointed out in previ-ous studies (11, 24). The phenotypes with respect to these cell be-haviors are consistent with our previous in vitro experiments (11)and were also verified via ex vivo inhibitor assays (fig. S5): (i) Thesimulations predicted that the NR invagination requires the properproportion ofNR to RPE regions (fig. S5, B andC), which correspondsto the dependence of the penetrance of cup formation on tissue sizes(24) and the phenotypes given under theWnt inhibitor IWP2 (fig. S5,F and I) and theWnt activators CHIR and BIO (fig. S5, G and I). Here,an overlarge proportion of the NR region (fig. S5B) prevented the in-vagination by increasing the energy gap to revert the NR curvaturefrom the apically concave to convex, while an excessively small pro-portion of the NR region (fig. S5C) prevented the NR invagination byreducing the total amount of cell proliferation. (ii) The simulationspredicted that frequent cell proliferation around the NR, observedin fig. S3, plays a key role in generating a driving force for the NR in-vagination (fig. S5D), which corresponds to the phenotype given byaphidicolin-induced cell cycle arrest (fig. S5, H and I). Here, the roleof the cell proliferation is to generate pushing forces on the surround-ing tissues, leading to a mechanical instability that buckle the NR toeither the apically convex or concave direction.
By screening the resulting in silico tissues with the magnitude oflocal tissue curvatures around NR and the NR-RPE boundary, wenarrowed down the parameters that provide the proper optic-cupshape (Fig. 1H, enlarged in fig. S4). This screening predicted twokey mechanisms that have not been previously mentioned and arenovel to the best of our knowledge (Fig. 1K): (i) The apically convexNR invagination is autonomously driven by the force generations
Okuda et al., Sci. Adv. 2018;4 : eaau1354 21 November 2018
of NR cells themselves, and (ii) the NR invagination is facilitated bythe force generations of NR-RPE boundary cells that actively con-strict along the apicobasal (lateral) direction. Further, we attemptedto verify each of these predictions experimentally.
Apical actomyosin reduction causes autonomous epithelialbending in the apically convex directionPreviously, we had suggested that the apically convex NR invagina-tion is driven by the bending force generated at the NR-RPE boundary(fig. S1A) (11, 25). However, in contrast, the present in silico screeningsuggests that NR would autonomously bend owing to the inversionof its spontaneous curvature (Fig. 2, A and B; figs. S4A and 6A; andmovie S5). It is well known that the increase in actomyosin accumu-lation on the apical surface causes apical constriction and bends ep-ithelial sheet in the apically concave direction (fig. S1C) (3–5, 17, 21).By reversing this concept, it could be possible that the reduction ofactomyosin accumulation on the apical surface relaxes the apicalcontractility and bends the epithelial sheet in the apically convex di-rection (Fig. 2A and fig. S1D).
To clarify this point, we investigated the residual stress within OVand NR. The in vitro NRs show variance in morphology dependingon its size at day 9 (24); some deform into a cup-like shape (Fig. 1A),and others maintain a spherical shape, even when vesicles have dif-ferentiated to Ceh-10 homeodomain-containing homolog (Chx10)+
NRs (Fig. 2C). We incised spherical OV and spherical NR usingmicro tweezers. As a result, the distal portion of the spherical OVmaintained its curvature, while the spherical NR buckled in the ap-ically convex direction (Fig. 2, C to F). This suggests that, while dif-ferentiating from OV to NR, cells generate the inner bending forceand the NR autonomously invaginates in an apically convexmanner.Consistently, the estimated bending rigidity of NR is much higherthan those of OV and RPE (Fig. 2G), implying that NR is unlikelydeformed by the external force generated at the surrounding tissues.Furthermore, as demonstrated in a previous report, the isolated hu-manNR autonomously inverted its curvature into an apically convexdirection (26). These results suggest that NR generates autonomousbending force in the apically convex direction.
In addition, as reported previously (11), the phospho–myosin lightchain (pMLC) accumulates at the apical surface of OV and RPE andis markedly reduced in NR during the in vitro and in vivo optic-cupformation (Fig. 2, H and I, and fig. S6, B and C). Therefore, we per-formed quantitative measurements of actomyosin distribution andepithelial curvature and revealed that the actomyosin reduction cor-relates with the epithelial curvature both in vitro (Fig. 2, J and K) andin vivo (Fig. 2K and fig. S6, E to G).
To address effects of the actomyosin reduction on the epithelialcurvature, we performed pharmacological assays of OV in vitro atlate phase 1 (Fig. 2L). The inhibition of myosin activity by the Rho-associated protein kinase (ROCK) inhibitor, Y27632, inverted thedistal portion of OV locally (Fig. 2M and movie S6), and maintainingmyosin activity using the inhibitor formyosin phosphatase, calyculinA(fig. S6D) (27), everted the distal portion of OV locally (Fig. 2N andmovie S6). In addition, the inhibition of the actomyosin reduction alsoprevented OV from invaginating in the ex vivo culture (Fig. 2O andfig. S6, H to L). Consistently, the ROCK inhibitor treatment on theinverted NR at phase 3 did not affect its morphology in both mouseand human embryonic stem cell–derived tissues (11, 26). These resultssuggest that actomyosin reduction could possibly cause apically con-vex epithelial invagination in optic-cup formation.
For further confirmation, we locally inhibited actomyosin accumu-lations onOV in early phase 1 and quantitativelymeasured the changesin the lengths of apical and basal surfaces (Fig. 2P andmovie S6); whilethe actomyosin inhibition extended both apical and basal surfaces, theapical extension was much larger than the basal one (Fig. 2Q). This
Okuda et al., Sci. Adv. 2018;4 : eaau1354 21 November 2018
suggests that the actomyosin reduction specifically relaxes apical con-tractility and generates bending force in the apically convex direction.Furthermore, by measuring the effective stiffness of apical surfaces,which reflects contractility, we clarify the positive correlation be-tween actomyosin accumulation and apical contractility (fig. S6M);
Fig. 2. Autonomous epithelial bending in apically convex direction due to apical actomyosin reduction. (A) The NR autonomous bending in the apically convexdirection driven by the inversion of NR spontaneous curvature. (B) In silico screening assay of optic-cup formation with respect to the NR spontaneous curvature (fig. S6Aand movie S5). Tissue morphologies are shown in the 3D coordinates with the distal-proximal, dorsal-ventral, and anterior-posterior axis. (C to F) Mechanical assays ofspherical OV at day 6 (D) and spherical NR at day 9 (E). The angle displacements by incising (F). (G) Normalized bending rigidities of OV, NR, and RPE estimated from theirapical elasticities and cell heights. (H) Immunostaining assay of pMLC in vitro. (I) pMLC distributions along the apicobasal (lateral) axis in (H). (J) Correlation between localpMLC intensity and curvature in epithelium shown in (H). (K) pMLC intensity on the apical side in the distal area, normalized by those in the proximal area, in vitro andin vivo. (L to N) Inhibitor assays of in vitro OV. (M) Inhibitor assay of in vitro OV with ROCK inhibitor, Y27632, at late phase 1 (movie S6). (N) Inhibitor assay of in vitro OVwith calyculin. (O) Invagination probability in in vitro and ex vivo cultures. (P andQ) Inhibitor assay of in vitro OV at early phase 1, where Y27632 was locally applied tothe distal portion of OV. The apical length, basal length, and height of the epithelium were measured (Q). Bars in (F), (J), (K), and (O) indicate SEs.
i.e., down-regulating myosin activity by Y27632 decreases OV stiff-ness, and up-regulating myosin activity by calyculin A increases NRstiffness.
These results strongly support the idea that actomyosin-dependentapical relaxation is a driving force of the NR autonomous bending,although myosin-dependent cellular activities and the mechanicalproperties of extracellularmatrices on the basal side, as reported in fishand chick embryonic optic cups (28, 29), may also contribute.
Lateral constriction amplifies epithelial curvature to form ahinge structureAlthough apical constriction is well known to bend epithelial sheets(3–5, 17), the in silico screening indicated that apical constrictiondistorts the epithelial sheet around the NR-RPE boundary (Fig. 3,A and D, and fig. S4B) and could not facilitate the NR invagination(Fig. 3E). As an alternative cell behavior, we assumed that lateral con-striction, whereby cells constrict along the apicobasal axis (Fig. 3A),may be involved. The simulations showed that lateral constrictionforms a smooth hinge structure along the NR-RPE boundary (Fig. 3Cand fig. S4B) and facilitates NR invagination (Fig. 3E and movie S7).
To address the difference in mechanical roles between apical andlateral constrictions, we theoretically estimated their effects on epi-thelial deformation by assuming single-cell mechanics (Fig. 3F).According to first-order estimations, the bending rigidity of epithe-lium hardly depends on apical strain but is markedly decreased bylateral strain (Fig. 3G), demonstrating that lateral constriction facil-itates epithelial curvature. Besides, when an epithelial sheet is alreadycurved like the NR-RPE boundary, lateral constriction plays a role inamplifying its curvature more effectively than apical constriction toform a hinge structure (Fig. 3H and fig. S1E). Furthermore, whileapical constriction shrinks apical surfaces of individual cells, lateralconstriction does not (fig. S6N); therefore, lateral constriction rathermaintains the smooth epithelial structure to form proper organ shape.
To clarify whether lateral constriction occurs during optic-cupformation, we observed the dynamics of epithelial thickness (corre-sponding to the lateral lengths of cells) in vitro and found that lateralconstriction certainly occurs at the NR-RPE boundary (Fig. 3I andmovie S8). While the epithelial thickness gradually decreases in anirreversiblemanner, it dynamically oscillates during the invaginationprocess (Fig. 3J). This oscillating lateral constriction had been un-known, whereas similar constrictions have been reported, such as os-cillating apical constrictions observed in Drosophila (30) and mousecleavage cells (31). In addition, nonoscillating lateral constrictions havebeen reported in a mathematical model (32), in Drosophila apoptoticcells (33), and in ascidian gastrulation (34).
To address the upstream regulation, wemonitored calcium activitythat is known to cause cell constriction (35, 36). As a result, we foundthat calcium transients occur specifically at the NR-RPE boundary(Fig. 3, K and L) and that the calcium transients correlated with lateralconstriction (Fig. 3, M and N, and movie S8). The lateral constrictionthat is correlated with calcium transients causes almost reversible de-formations (Fig. 3M), and the time scale of their frequency is muchsmaller than that observed in the prolonged observation of the mac-roscopic tissue deformations (Fig. 3J). This implies that the accumu-lation of the short-term reversible constriction leads to the long-termirreversible constriction in a plastic manner.
We also found that the calcium transients propagate from the basalto apical surfaces within cells (Fig. 3O). In addition, we visualized actincytoskeletons using LifeAct (37) and noticed a characteristic structure
Okuda et al., Sci. Adv. 2018;4 : eaau1354 21 November 2018
of actin fibers aligning along the apicobasal axis in NR-RPE boundarycells (Fig. 3P andmovie S9). Actin fibers normally accumulated on theapical side of epithelial cells such as those in OV cells (Fig. 3Q) andRPE cells (data not shown). Because calcium triggers cell contractionsby regulating actin-myosin interactions (35, 36), these results implythat the lateral constriction is driven by actomyosin contractility andis triggered by calcium activity on the basal surface.
Strain-triggered cell constriction facilitates epithelialinvagination as a mechanical feedbackAs shown above, during optic-cup formation, NR cells autonomouslygenerate bending force, and subsequently, NR-RPE boundary cellscause lateral constriction to form a hinge structure. We consideredthe possibility that these two behaviors might be mechanically linked(fig. S1A); the bending force generated at the NR region propagates tothe NR-RPE boundary and triggers lateral constriction via cellularmechanical strain (which we refer to as strain-triggered constriction).
We first investigated whether the bending force generated at theNR region triggers cells at the NR-RPE boundary to facilitate NR in-vagination. To clarify this point, we artificially exerted the mechanicalforce on OV, imitating the effect of NR autonomous bending on theNR-RPE boundary; by pushing a thick micropipette on the epithelialsurface of OV, we forcedly deformed a distal portion of the epitheliumto be apically convex and the surrounding portion to be apically con-cave (Fig. 4, A and B). The epithelia expressed an elastic response tothe brief pushing, whereas they expressed a plastic response to sus-tained pushing over a longer time; while pushing the epithelia, theconcave region of the epithelia gradually became acute (Fig. 4B andmovie S10). The acute shape was maintained even after removingthe pipette (Fig. 4, C and D). These results suggest that the epitheliaexpress a time-dependent rheological response to external force, whichplays a role in adaptively facilitating NR invagination during optic-cupmorphogenesis.
Since the lateral constrictions correlated with calcium transients inthe optic-cup formation (Fig. 3, L to N), we further examine whetherthe bending force generated at NR causes calcium transients selec-tively at the NR-RPE boundary. To address this point, we observedcalcium transients in the artificially deformed OV. The frequency ofcalcium transients increased at the apically concave region but not atthe apically convex region (Fig. 4, E to H). Moreover, these calciumtransients propagated from the basal to the apical sides (Fig. 4I), sim-ilar to the cells at the NR-RPE boundary (Fig. 3O). These results sug-gest that the time-dependent mechanical response of the epithelium(Fig. 4B) may be triggered by calcium transients, corresponding withprevious reports that inhibiting calcium prevents cell constriction (38)and optic-cup formation (39).
On the basis of calcium activity (Figs. 3O and 4, E to I), we expectedthat the cells at the NR-RPE boundary sense mechanical stress ontheir basal surfaces generated by autonomousNR bending. To clarifythis point, shear stress was exerted on the basal surface ofOVby gentlyscratching it with a glass needle, andwe found that the shear stress onthe basal surface triggers calcium transients (Fig. 4, J and K, andmovie S11). Consistently, inhibiting focal adhesion kinases that arerelevant to themechanosensing on the basal surface (40) by PF573228reduced the frequency of calcium transients (Fig. 4H). Moreover, toclarify effects of calcium transients on lateral constriction, we locallyinduced calcium transients using laser ablations according to the re-ported method (41) and revealed that the local up-regulation of intra-cellular calcium concentration drives lateral constriction (Fig. 4, L to P,
Fig. 3. Calcium-dependent lateral cell constriction in epithelial hinge structure formation. (A) Concept of apical and lateral cell constrictions at the NR-RPE bound-ary. (B to E) In silico screening assay of optic-cup formation with respect to the apical and lateral cell contractility (movie S7). External view of the entire tissue and thesections around the NR-RPE boundary obtained under conditions with no constriction (B), lateral constriction (C), and apical constriction (D). Dependence of NR curvatureon apical and lateral constrictions (E), where apical and lateral constrictions are expressed as the length strains of the spontaneous perimeter and height of cells (non-dimensions). Tissue morphologies are shown in the 3D coordinates with the distal-proximal, dorsal-ventral, and anterior-posterior axis in (B) to (D). (F to H) Theoreticalanalyses of cell mechanics; a simplemathematical model of cell mechanics based on assuming a conical frustum as an average cell shape (F). Epithelial bending rigidity asa function of apical/lateral strain (G). Sensitivity of epithelial curvature to apical/lateral strain as a function of the reference curvature of epithelium (H). (I and J) Time-lapseimaging of the in vitro optic cup at the NR-RPE boundary (movie S8). Time displacement of epithelial height (J). (K and L) Calcium observation in the in vitro optic cup;time variance of local GCaMP intensity at NR, RPE, and the NR-RPE boundary (L). (M and N) Kymographs of GCaMP intensity and cell shape along the apicobasal axis,respectively. (O) Time-lapse imaging of calcium transients within a single cell. (P and Q) Actin accumulation within individual cells (movie S9). Actin aligning along theapicobasal axis in the NR-RPE boundary (P) and actin accumulated around the apical surface in OV (Q). DIC, differential interference contrast.
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Fig. 4. Strain-triggered cell constriction in epithelial folding. (A to I) Mechanical assay in the in vitro OV using a micropipette (movie S10); the distal portion of thevesicle forcedly invaginated, and the surrounding portion is forcedly folded (A and B). The pipette was gently removed after sustained pushing for 30 min (C). Enlargedframes in (B) and (C) show the time-lapse images of the folded region of the epithelium. (D) Difference in the epithelial angles before and after pushing for 30 min in (B)and (C). (E and F) Calcium distribution and local dynamics in (B). Arrows in (F) indicate the peaks of GCaMP intensity corresponding to calcium transients. (G) Time-lapseimages of calcium transients in a single cell around the folded region under pushing. (H and I) Spatial distribution of the calcium transient events under pushing (H),from which the average frequencies are counted in each region (I). (J and K) Time-lapse imaging of calcium responses to shear stress on the basal surface (movie S11).(L to P) Time-lapse imaging of single-cell dynamics under the assay of focusing two-photon laser locally on the basal cell surfaces (movie S12) (41): single-cell shape (L),epithelial height (M and N), and calcium concentration (O and P). (Q to T) Proof of concept by computational simulations under the condition with the strain-triggeredlateral constriction using the 3D vertex model; in silico optic cup obtained by the simulation at t = 48 (R) (movie S13), probability density of strain-triggered lateralconstriction along the proximal-distal axis (S), and dependence of NR curvature on lateral contractility (T). Tissue morphology is represented in the 3D coordinates withthe distal-proximal, dorsal-ventral, and anterior-posterior axis in (R). In (R) and (T), lateral constriction is expressed as the length strain of the spontaneous height of cells(nondimensions). (U) Proposed model for the stepwise optic-cup morphogenesis with the strain-triggered mechanical feedback. Bars in (D), (I), (N), and (P) indicate SEs,and bars in (T) indicate SDs.
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and movie S12). These results suggest that lateral constriction may betriggered bymechanical strain via calcium transients based on cellularmechanosensing on the basal surfaces.
Last, for the proof of concept of the strain-triggered cell constric-tion, we performed further computational simulations using the 3Dvertex model. On the basis of the experimental results (Figs. 3O and4, A to P), we assumed that the tensile strain of cell surfaces on thebasal side triggers transient lateral constriction (Fig. 4Q). As a result,the simulations successfully recapitulated optic-cup formation (Fig. 4Rand movie S13), wherein the strain-triggered lateral constrictionautonomously occurred at the NR-RPE boundary (Fig. 4S) and facili-tated the NR invagination (Fig. 4T).
In summary, our results suggest that the mechanical force plays akey role as a feedback regulator in self-organizing the 3D optic-cupformation (Fig. 4U). During optic-cup formation, OV autonomouslygenerates the differentiation pattern of NR andRPE. According to thedifferentiation, the NR reduces actomyosin accumulation and causesautonomous bending in the apically convex direction. The macro-scopic bending force propagates to the NR-RPE boundary region,generates mechanical strain on individual cells across different scales,and triggers lateral constriction via mechanosensing on the basal cellsurfaces. The lateral constriction forms a hinge structure along the NR-RPE boundary and facilitates NR invagination as a mechanical feedback.
on October 15, 2020
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DISCUSSIONIt has long been known that diffusible molecules are key players inproviding signals between cells during embryogenesis. While themolecular signaling has been successfully explained, many aspectsof morphogenesis, including the regulation of macroscopic 3D tissuedeformation, remain unclear. For example, cellular force generationdriving morphogenesis had been thought to be triggered by molec-ular cues according to cell differentiation patterns, but the presentstudy has revealed that the hinge structure formation along the NR-RPE boundary is actually triggered bymechanical strain viamechano-sensing during optic-cup formation (i.e., mechanical force plays a keyrole in feeding back the 3D tissue deformation to the force generationsof individual cells across different scales). A complete understandingof this molecular mechanism requires further investigation, but thisfinding challenges the conventional thought process about the devel-opment of multicellular organisms. The role of mechanical force inmulticellular communication via macroscopic epithelial deformationhas been suspected since the pioneer computational work in 1981 (42),and the present study is probably the first study to the best of ourknowledge to identify this role in living tissue development.
The present study has provided several findings relevant to epithelialmechanics such as the mechanism of the myosin reduction–inducedapically convex invagination and the role of myosin-dependent lateralconstriction. These findings can be attributed to the versatility andpredictability of the developed 3D vertex model. Besides the optic-cup formation, this model can also be applied to various physiologiesin morphogenesis, homeostasis, and disease. While this model hasbeen validated from physical and topological points of view (18, 23),further validations are required in several points such as the applicablerange of the model and the quantifiability of its predictions, in prac-tical uses to each biological phenomenon.
The present study has also suggested that mechanical force playsa role in causing feedback during optic-cup formation. Since themechanical feedback occurs adaptively according to the 3D tissue
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deformation, it may have a role in sustaining the robustness of mor-phogenesis. In particular, in the optic-cup formation, it may play akey role in robustly forming the smooth hinge structure along theNR-RPE boundary under environmental disturbances; at least in thein vitro culture system of optic cups, the location of the NR-RPEboundary largely varies (24). Because the presence of a hinge structureis observed in a variety of boundaries between different tissues, theeffect of mechanical feedback is likely to be often involved in self-organizing developmental processes.
The mechanical feedback between cells is a typical example ofphenomena emerging from the multicellular dynamics comprisingdynamic intracellular systems [referred to as cytosystems dynamics(17)]. Because the multicellular dynamics involve nonlinear effectsof multicellularity, it is difficult to predict the integrated dynamicsfrom individual cell behaviors. For example, while the existence ofthe lateral constriction in optic-cup formation might have been pre-dictable, its role in forming the smooth hinge structure had been un-expected (Fig. 3, A to E). The complementary approach of in vitro andin silico systems used in the present study has helped to partly over-come the challenges. This complementary approach could be appliedwidely to explore new aspects of the biological nature of multicellularsystems and for predicting their dynamics. This approach may alsoopen up a new avenue in the field of highly organized tissue engineer-ing, providing a basis for manipulating the 3D structure of stem cell–derived tissues.
MATERIALS AND METHODSIn vitro and ex vivo culturesIn vitro optic cup was derived using serum-free floating culture ofembryoid body-like aggregates with quick reaggregation (SFEBq)culture, as described previously (11). The optic-cup formation hasbeen successfully recapitulated in several laboratories (11, 24, 43).Ex vivo culture was performed by excising the heads of embryonicday 9 mouse embryos and incubating them in Dulbecco’s modifiedEagle’s medium and F-12 nutrient mixture supplemented with N2and penicillin additive under 40% O2 and 5% CO2.
Observation of single-cell shapes in vitroSingle-cell shapes in the regions ofNR and theNR-RPE boundarywereobtained from the organoids at day 9 in the mixed culture of Rx–GFP(green fluorescent protein) and Sox1-GFP cell lines. Because Rx-GFPcells generate positive fluorescence but Sox1-GFP do not in the opticregion, cells in the organoid generate fluorescence in a mosaic manner(11). We obtained their images using a two-photon fluorescence mi-croscopy (Olympus) and extracted cell shapes using the image process-ing software (ZEISS, Imaris).
Quantification of epithelial curvature, height, andsignal intensityThe epithelial curvature, height, and signal intensity were measuredfrom the immunostaining images of sliced tissues and/or the confocalimages of whole tissues, where the curvature is measured by a sequen-tial three-point method (12).
ImmunohistochemistryImmunohistochemistry was performed as described previously. Anti-bodies against the following proteins were used at the indicated dilutions:Chx10 (sheep/1:1000, Exalpha Biologicals), microphthalmia-associated
transcription factor (Mitf) (mouse/1:1000, Exalpha Biologicals), andpMLC2 (rabbit/1:50, Cell Signaling Technology). DAPI (4′,6-diamidino-2-phenylindole) was used for counterstaining the nuclei (MolecularProbes). Stained sections were analyzed with an LSM780 ConfocalMicro-scope (Carl Zeiss).
Measurements of cell stiffnessThe cell stiffness was examined by indentation assay using an atomicforce microscopy (AFM) cantilever as described previously (11), whereOV and NR regions were defined on the basis of the GFP fluorescenceof Rx-GFP lines and tissue structures on days 7 and 9, respectively. Sim-ilarly to surface stiffness, surface contractility wasmeasured usingAFM,since, in the use of AFM, the displacement of cantilever ismeasured andcan be translated into contractility and stiffness (44).
Mechanical perturbation and calcium observationMechanical perturbations on OVs were examined using thin- andthick-glass micropipettes, whose diameters were 10 and 100 mm, re-spectively. The calcium concentration was observed via invertedmicro-scopes (confocal or multiphoton) combined with a full-sized CO2/O2
incubator (Olympus) using mouse embryonic stem cells on the Sox1-GFP cell line in which the GCaMP3 gene is knocked-in on the Rosa26locus. As Rx-GFP cells generate positive fluorescence but Sox1-GFPcells do not in the optic region, cells in the organoid generate fluores-cence in a mosaic manner. For the quantification of calcium transients,we regarded that a calcium transient occurs when the GCaMP intensityexceeds the threshold and counted the number of transients per unittime and area. The threshold was defined as the multiple values ofthe SD of GCaMP intensity more than the average in each sequenceof images. The frequency was measured after processing the imagesvia the median, Gaussian, Laplacian, and banalization filters. Local in-duction of calcium transients was completed with the same multi-photon optical system for 3D live imaging, where the 900-nm laserbeam from Mai Tai eHP DeepSee was condensed at target cells viaa ×25 water immersion lens (numerical aperture, 1.05) using a spotillumination or line scan (typically 0.1 to 0.5 s duration). Mechanicalstimulation was performed using sharp-pointed glass micropipettescontrolled by a piezomanipulator (MM3A-LS,KleindiekNanotechnik)under the invertedmicroscope combined with a spinning disc confocalunit (CSUW1, Yokogawa).
Theoretical analyses of epithelial propertiesand deformationOn the basis of the mean field approximation of the epithelial sheet(17, 45), we assumed that an average cell shape embedded in a mono-layer epithelial sheet is a conical frustum, whose apical and basal radiiand height are represented by ra, rb, and h (Fig. 3F). The curvature ofthe epithelial sheet, represented by c (positive in the case of apically con-cave and −2/h < c < 2/h), was obtained as c = (2/h)(rb − ra)/(rb + ra).Weassumed that cells cause apical and lateral constrictions, whose activestrains on apical perimeter and height are represented by ga and gl, re-spectively (negative in the case of constriction).We represent the apicalcell surface area before apical and lateral constrictions by sa ref. The ap-ical surface area, represented by sa, was given by sa/sa ref = (1 − ga)
−2 inthe case of apical constriction and sa/sa ref = 1 in the case of lateral con-striction (fig. S6N).
On the basis of continuum mechanics, the bending rigidity of theepithelial sheet was estimated as the bending rigidity of beams withhomogeneous elasticity for individual tissues.We represent the bending
Okuda et al., Sci. Adv. 2018;4 : eaau1354 21 November 2018
stiffness before apical and lateral constrictions byGref. Bending rigidityof plate, represented byG, can be expressed byGº Eh3, where E is anelastic module. Immediately, we obtainedG/Gref = 1 in the case of ap-ical constriction andG/Gref = (1− gl)
3 in the case of lateral constriction(Fig. 3G). Similarly, the ratio of the bending stiffness of OV, NR, andRPE was estimated from the experimental data of cell heights and ap-ical elasticity (Fig. 2G).
The dependence of the epithelial curvature on the apical and lateralconstrictions can be expressed as the partial differential equations of cfor these active strains as follows
∂c∂ga
�����ga¼0
¼ � 1h
1� hc2
� �2( )
ð1Þ
∂c∂gl
�����gl¼0
¼ �c ð2Þ
These results are shown in Fig. 3H. The functions in Eqs. 1 and 2intersect at 2ð ffiffiffi
2p � 1Þ=h in c > 0. In the case that epithelial sheet is
almost flat (c < 2ð ffiffiffi2
p � 1Þ=h), apical constriction ismore effective onthe curvature than lateral constriction for increasing the curvature. Onthe contrary, in the case that epithelial sheet is already bent (c >2ð ffiffiffi
2p � 1Þ=h), the lateral constriction is more effective to facilitate
the curvature.
Computational simulations using a versatile 3D vertexmodel of optic-cup formationThe 3D multicellular dynamics were expressed using the versatile 3Dvertex model (fig. S2). The main symbols in this model are listed intable S1. In this model, each cell shape is represented by a single poly-hedron, and each cell-cell boundary is represented by a polygonal face(fig. S2, A and B) (13). Because the polygonal faces are shared byneighboring polyhedrons, the entire tissue structure is represented bya single network composed of vertices and edges (fig. S2C).
Topological dynamics of 3D multicellular dynamics such as cellrearrangement, division, and apoptosis were expressed by severaltypes of network reconnections. Cell rearrangement is expressed byreconnecting local network patterns using the reversible network re-connection model (fig. S2D). Previously, we have mathematicallyproved a part of physical validities of this model; i.e., this model canexpress continuous cell rearrangements with geometric and energeticreversibility (18). Cell proliferation was expressed using a cell prolif-erationmodel that expresses cell proliferation by cell growth (increasein cell volume) and cell division (increase in cell number; fig. S2E)(46). Cell apoptosis was expressed using a cell apoptosis model thatexpresses cell apoptosis by cell shrinkage (decrease in cell volume)and cell disappearance (decrease in cell number; fig. S2F) (47). Pre-viously, we have also mathematically proved a part of topological va-lidities of this model; i.e., this model can express the entire pattern ofmulticellular topological dynamics in 3D space (23). This model hasbeen applied to several 3D multicellular dynamics (48–51) and canpotentially be applied to various physiologies in morphogenesis, ho-meostasis, and disease.
The 3Dmulticellular dynamics were expressed by the vertexmove-ments according to the total energy, represented by U. As the defor-mation process of the optic-cup formation takes approximately 2 days,we regarded it as the quasi-static process from a thermodynamic point
of view, where viscous forces are relaxed in an instance. Under thisprocess, the energetic force satisfies the force balance at each timepoint as ∇∇∇U = 0. Here, we defined the total energy as U = U({ri},{zja}, {xjkb}), where {…} indicates a set of components, ri is the positionvector of the ith vertex, zja is the ath physical parameter of the jth cell,and xjkb is the bth physical parameter of the jth and kth cells. Under∇∇∇U = 0, the vertex locations {ri} at each time point are obtained byseeking the local minimum of U, and thereby the time displacementsof the vertex locations {ri} are obtained as the changes in {ri} againstthose in physical parameters {zja} and {xjkb}. The local minimum ofUis solved by the Euler method of the overdamped equation (52).
We introduced the jth cell volume vj, height hj, apical perimeterlength pj, basal surface area sbj, total surface area stj, and the apicaledge between jth and kth cells lajk, as a function of {ri}. The totalenergy function U is expressed as follows
UðfrigfzjagfxjkbgÞ ¼
∑cell
jKvj
vjveq j
� 1
� �2
þ ∑cell
jKhj
hjheq j
� 1
� �2
Hðhj � heq jÞ þ
∑cell
jKa j
pjpeq j
� 1
!2
þ ∑cell
j∑cell
kð>jÞlg jkla jk þ
∑cellj Kbj
sbjsbeq j
� 1
� �2
þ ∑cellj ks jst j ð3Þ
where H is the Heaviside step function with a value of 1 when thevariable is positive and 0 otherwise. In Eq. 3, the first term denotesthe elastic energy of individual cell volumes, where Kvj and veqj arethe jth cell volume elasticity and equilibrium volume, respectively. Thesecond term is the elastic energy of individual cell heights (fig. S2G),where Khj and heqj are the jth cell height elasticity and equilibriumheight, respectively. The third term is the elastic energy of individualcell apical perimeters (fig. S2H), where Kaj and peqj are the jth cell ap-ical perimeter elasticity and equilibrium apical perimeter length, re-spectively. The fourth term is the boundary length energy betweencells on the apical surface (fig. S2I), where lgjk is the apical edge lengthenergy between the jth and kth cells. The fifth term is the elasticenergy of individual cell basal surfaces (fig. S1J), where Kbj and peqjare the jth cell basal surface elasticity and equilibrium basal surfacearea, respectively. The last term is the total surface energy of individ-ual cells (fig. S2K), where ksj is the jth cell surface elasticity. Hence, inEq. 3, {zja} is described as a set of parameters Kvj, Khj, Kaj, Kbj, ksj, veqj,heqj, peqj, and sbeqj, and {xjkb} is a set of lgjk.
The optic cup is formed even under the conditionwhere the root oftheOV is cut (11), and the shape of the root of theOV is not importantfor morphogenesis. Hence, the initial condition was set to be a mono-layer spherical OV. The initial OV is composed of 1600 cells, whichwas estimated from the tissue size and cell density measured in ex-periments. In the initial OV, the dorsal-ventral and distal-proximalaxes are defined to be orthogonal in the 3D orthogonal coordinates.Moreover, the optic cup is formed even under conditions where a holeis made in the epithelial sheet or the surrounding tissues are removed(11); therefore, the inner pressure and extrinsic forces are unnecessary.Hence, the boundary condition was set to be free with fixing the centerof all vertex positions on the coordinates.
By varying all the unknown parameters, we obtained a standard setof physical parameter values (table S4) that recapitulates the optic-cup
Okuda et al., Sci. Adv. 2018;4 : eaau1354 21 November 2018
formation (Fig. 1, I to L). We also varied all of the unknown param-eters around the standard values and obtained many phenotypes(table S5 and fig. S4). The resulting optic cups were screened by twoevaluation parameters: the NR curvature and the NR-RPE boundarycurvature, represented by cNR and cB, respectively (closed regions infig. S4). By varying cNR and cB, we determined several dominantphysical parameters for the proper optic-cup formation, from whichFigs. 2B and 3 (B to E) were extracted.
To test whether the strain-triggered mechanical feedback is in-herited in the optic-cup formation, we modeled this cell responseand implemented it to the above model for the in silico screening byreplacing the part of lateral constriction (Fig. 4Q). Because the lateralconstriction oscillates in the optic-cup formation, we expressed thatcells transiently constrict depending on the basal surface strain andrelax for a while. In biological experiments, the basal calcium transientsin NR are much lower than those in OV and RPE, since the gap junc-tion is poor in NR (53); hence, we assumed that this strain-triggeredconstriction occurs only in the OV and RPE regions. By varying therelevant physical parameters, we obtained the optic-cup morphogene-sis that contains the mechanical feedback (Fig. 4, R to T). Details of themodel are described in Supplementary Text.
Numerical calculations were performed using customized C++software on a computer comprising 2.9-GHz Intel Xeon dual processorsand 64-GB random-access memory and RIKEN Super CombinedCluster. The results were visualized with ParaView (54).
SUPPLEMENTARY MATERIALSSupplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/11/eaau1354/DC1Supplementary TextFig. S1. Concept models of optic-cup formation and epithelial bending.Fig. S2. Versatile 3D vertex model describing multicellular dynamics in 3D space.Fig. S3. Quantification of optic-cup morphogenesis.Fig. S4. Quantitative simulations of optic-cup morphogenesis for all of the unknownparameters.Fig. S5. Comparison between in silico and ex vivo optic-cup formation under perturbations.Fig. S6. Actomyosin activities in in vivo and ex vivo optic-cup morphogenesis.Table S1. Main symbols used in the 3D vertex model of optic-cup formation.Table S2. Standard physical parameter values of cell states in computational simulations ofoptic-cup formation.Table S3. Standard physical parameter values of boundary regions in computationalsimulations of optic-cup formation.Table S4. Standard physical parameter values of cell behaviors used in computationalsimulations of optic-cup formation.Table S5. Varied physical parameter values obtained from computational simulations ofoptic-cup formation.Movie S1. Hinged cell shape at the NR-RPE boundary in the in vitro optic cup.Movie S2. In silico recapitulation of optic-cup morphogenesis using the versatile 3D vertexmodel.Movie S3. Cell proliferation, constriction, and apoptosis in in silico optic-cup formation.Movie S4. Dependence of in silico optic-cup morphogenesis on cell heightening, proliferation,apoptosis, and differentiation.Movie S5. Dependence of in silico optic-cup morphogenesis on formation of spontaneouscurvature of NR.Movie S6. Pharmacological assays of actomyosin activities in vitro.Movie S7. Dependence of in silico optic-cup morphogenesis on apical and lateral cellconstrictions.Movie S8. Lateral cell constrictions in vitro.Movie S9. Characteristic alignment of intracellular actin fibers along the apicobasal axis in vitro.Movie S10. Elastic and plastic responses of in vitro neuroepithelium to mechanical stimuli.Movie S11. Calcium response to shear stress on the basal surface in vitro.Movie S12. Lateral constrictions triggered by local up-regulation of intracellular calciumconcentration in vitro.Movie S13. In silico recapitulation of optic-cup morphogenesis with strain-triggered lateralconstriction.
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Acknowledgments: We are grateful to S. Hayashi for critical reading and invaluablecomments and to all the laboratory members for fruitful discussions. This articleis dedicated to the memory of the late Dr. Yoshiki Sasai. Funding: This research wassupported by JST/PRESTO grant number JPMJPR16F3 (to S.O.), JSPS KAKENHI grantnumbers 16H04799 and 16H06485 (to M.E.), Research Center Network for Realization ofRegenerative Medicine of AMED (to M.E.), and Strategic Programs for R&D (President’sDiscretionary Fund) of RIKEN (to M.E.). Author contributions: S.O., M.E., and Y.S. conceivedand designed this study. S.O. and M.E. performed experiments, image processing,experimental data analyses, and theoretical and computational analyses and wrote themanuscript. N.T., Y.H., and M.K. also performed experiments. Y.I. and T.A. discussedtheoretical and computational analyses. Competing interests: The authors declare thatthey have no competing interests. Data and materials availability: All data needed toevaluate the conclusions in the paper are present in the paper and/or the Supplementary
Okuda et al., Sci. Adv. 2018;4 : eaau1354 21 November 2018
Materials. Additional data and source codes related to this paper may be requested fromthe authors. The Rx-GFP cell line is available from RIKEN BioResource Research Center(ID: AES0145). The Sox1-EGFP-GCaMP3 cell line will be deposited at the cell bank of RIKENBioResource Research Center.
Submitted 9 May 2018Accepted 19 October 2018Published 21 November 201810.1126/sciadv.aau1354
Citation: S. Okuda, N. Takata, Y. Hasegawa, M. Kawada, Y. Inoue, T. Adachi, Y. Sasai, M. Eiraku,Strain-triggered mechanical feedback in self-organizing optic-cup morphogenesis. Sci. Adv. 4,eaau1354 (2018).
Strain-triggered mechanical feedback in self-organizing optic-cup morphogenesisS. Okuda, N. Takata, Y. Hasegawa, M. Kawada, Y. Inoue, T. Adachi, Y. Sasai and M. Eiraku
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